Physics corner – 29ers v 26ers – am I right?

OK the accepted wisdom is that 29ers accelerate more slowly. But do they?

Looking at wheel size alone, energy is proportional to the moment of inertia (MOI) and the square of the angular rotational speed (w).

i.e. e ~ MOI x w^2

Now…MOI = (integral of) mass x (distance from COG)^2

So a 26er wheel has ~10% less mass (as regards MOI) as an identical 29er wheel. The distance of that mass from the COG si 10% greater. So the MOI of the 29er wheel is 10% greater.

But at the same (bike) speed the 29er wheel is rotating 10% more slowly, so the energy of the 29er wheel is: 10% less than the 26er

So a 29er wheel actually takes less energy to accelerate to the same speed. This can’t be right?

Black=white, you are a genius 😀

Oops I see I should also look at the linear kinetic energy required also – which would obviously be greater for the 29er – but enough to tip the scales?

I think I need a coffee first.

Angular speed decreases linearly with increased wheel diameter, angular momentum increases with the square of diameter, so the ease of acceleration decreases linearly in response to increasing diameter. Add increased mass and bigger wheels definitely require more force to accelerate at an equal rate but are better at maintaining their speed because of this.

Oops I see I should also look at the linear kinetic energy required also – which would obviously be greater for the 29er

And which tyres were used of course.

I don’t understand the complicated maths above.

As a layman’s explanation…
The two bikes are travelling at the same speed, therefore the surfaces of the tyres are travelling at the same speed.
However, any point on the 29er tyre (say, an individual tread block) has got to travel 10% further to get back where it started, plus there are more tread blocks.
So, moving more mass over a greater distance has got to take more energy hasn’t it ?

Not necessarily, kinetic energy is half M V squared, so you get punished the faster you go, so 26ers need to rotate faster for the same speed so need more energy to achieve that speed.the trade offs favour 29ers, but it is very marginal.

The real benefits of 29ers seems to be the fact they roll better over terrain. So every pebble, stone, undulation – I.e thousands, even millions of imperfections over the course of a ride, takes out less energy from your forward momentum, and all these tiny, fractional amounts add up to something significant over the course of a long ride. And for the rider, less energy they need to input.

Done a few rides on my 29er now and don’t notice much of a difference in acceleration between it and my 26er hardtail. Both bikes are lightish XC hardtails. The difference once the bikes are up to speed is far more discernable – 29er just keeps on rollin’

its quite sad reading all these stats when all most of us want to do is enjoy riding our bikes, which is something i wouldnt if all i was concered about was if im rolling better over this tree stump… 🙄

MidlandTrailquestsGraham, the surfaces of the tyres are the same, but the rpm of the wheel is lower for the 29er, therefore you need to accelerate the 26er wheel more to achieve the same speed, and the relationship between energy input and acceleration is not linear. The higher the speed you want to accelerate to the more and more energy you need to input. So the argument about accelerating the extra weight of a 29er is not necessarily true. It is either cancelled out by the lower speed of a 29 inch wheel, or benefits a 29 inch wheel.

However, any point on the 29er tyre (say, an individual tread block) has got to travel 10% further to get back where it started, plus there are more tread blocks.

Yeah it takes more energy for a turn of the wheel – but the bike has travelled further too.

I look at it this way:
* since energy can’t be created or destroyed, 26ers and 29ers are equally efficient (on a flat surface). All the energy the rider puts in, they get back, tho perhaps the profile of how it is put in and got back are different. ie the 29er takes more energy to get to speed but rolls further once it’s there.
* but trails aren’t flat. All the trailcrap (roots, loose surface, stones) cost energy and impede progress. But they impede the 26er more. Since our trails are littered with trailcrap, this can add up to a big difference over a ride of any distance.

Make sense?

cynic-al, the intertia of the 29er wheel is higher by 10% because of the mass (assuming the rim and tyre weight the same per cm) and 10% squared higher because of the distance from the hub. So overall, it’s 10% cubed. While the speed of rotation is only reduced by 10%, as it’s a straight linear relationship with circumference (or radius). So on balance, the 29er is worse by 10% squared.

For the same reason, a Brompton with 16″ wheels accelerates really well, on a smooth road.

What’s 10% squared?

It can’t be 10×10 = 100% nah

It can’t be 0.01 x 0.01 = 0.0001 = 0.1%

?

its quite sad reading all these stats when all most of us want to do is enjoy riding our bikes, which is something i wouldnt if all i was concered about was if im rolling better over this tree stump…

So don’t read the thread? What were you expecting from a thread marked “Physics Corner”?

Fortunately for you, there are people who are interested in the physics of bikes, which is why today’s bikes are so enjoyable to ride.

This is like one of those questions on university challene whee you can’t even begin to comprehend the question to guess an answer let alone work it out.

What’s 10% squared?

you want 110% squared

yeah of course, doh

1.1 x 1.1 = 1.21 or 21%

ta

Talk about over complicating things!!

The rider of the bike with the bigger wheel (assuming the same gearing) will have a lower mechanical advantage, so acceleration will be less for the same energy applied.

So you fit a rear cassette and/or crankset to mitigate this. I won’t do the maths!

I would think that an individual should opt for a size of bike that suits their anatomy and that wheel size should be part and parcel of this. So if you are a short arse, stick to small frames, small wheels. If you are long legged and rather tall, choose a large 29er frame with the bigger wheel sizing.. Simples!

Spongebob, it isn’t that simple as I already explained. When your bike is moving it has linear kinetic energy and rotational kinetic energy (the flywheel effect of your wheels). The bigger your wheels, the more rotational kinetic energy they contain. This means that it is harder to accelerate a bigger wheeled bike (because you have to add extra energy) but that the bigger wheeled bike is better at maintaining speed in the rough (because it also resists negative acceleration more strongly).

Ride a BMX or a Brompton after riding a MTB or roadbike and the pros and cons of different wheel sizes become way more obvious than from the more marginal difference between 26er and 29er!

As chiefguru + the increase in mass which i anticipate (id put money on it) increasing at a greater rate than linear in respect to wheel diameter to attain equal strength and stiffness.

[quoteSo don’t read the thread? What were you expecting from a thread marked “Physics Corner”?

Fortunately for you, there are people who are interested in the physics of bikes, which is why today’s bikes are so enjoyable to ride.[/quote]

I think you are missing the point…second thoughts forget it I can’t be arsed

Stan’s crest rims:
26er = 340g
29er = 380g

Racing Ralph 2.1 EVO, 26″ = 465g
Racing Ralph 2.1 EVO, 29″ = 495g

(+Spokes? But they’re not at the rim so matter less).

Total difference about 9%.

Cheers greybeard, I see my error now – should have had the coffee first d’oh! what an idiot!

andypaul I don’t see your point either, but don’t worry about it.

[quoteandypaul I don’t see your point either, but don’t worry about it.[/quote]

Lol, we all have our off days.. 😳

😀

I am crap at Physics but I know ALL bikes are fun to ride, I don’t think Physics comes into the equation 😉

TBH, the acceleration of the average bike is only limited by the flat blob of lard sat on said bike…………..

if we really want to answer the 29er debate, someone is going to have to build a “terrain” simulator that means we can accurately measure the drag torque on a 26 and 29 inch wheel over various types of surfaces. Think of a treadmill, but instead of a smooth belt, one which can be swapped out to have various sized surface artifacts attached to it. So we start with a smooth belt, measure the delta torque, then say 1mm bumps, then 3mm bumps, then 5mm bumps etc etc till we are all absolutely sick to death of the subject! (What? you’re sick to death of it already? me too!!! 😉

All this is well over my head!

My own experience has shown my 29er is faster on what I would call “xc” type stuff, I.e. no sudden acceleration, steep stuff or sharp turns. But on more technical riding, wheel flex and slower acceleration makes for slower lines and less ability to really attack aggressively.

Yes, bigger diameter wheels are heavier and require more force to accelerate , so unless you have unlimited power they are slower .

I’m disappointed – I expected to see something about ghosts

Yes, bigger diameter wheels are heavier and require more force to accelerate , so unless you have unlimited power they are slower .

No they are slower to accelerate but also slower to decelerate which makes them faster when carrying speed is more critical – but slower when changing speed is more critical.

No they are slower to accelerate but also slower to decelerate which makes them faster when carrying speed is more critical – but slower when changing speed is more critical.

but on virtually all courses, accelerating (to speed up, slow down or turn corners) is important. You need to think about what is the result of having heavier, larger diameter wheels in practical terms. Maybe if you want to achieve a speed record down a straight hill then OK, but back in the real world, the physics says bigger wheels slower / need more power

There is a good reason why, ever since the dawn of the bike, manufactures have tried to make wheels as light as possible. The momentum advantage from weight alone is never enough to overcome the extra force required to accelerate that wheel in practice. As long as you don’t compromise on stiffness a lighter wheel of the same radius is always better. Where this gets complicated with 29ers is that the larger radius means that they are decelerated less by obstacles. The advantage comes from the size not the extra mass though and you’d still want a 29er wheel to be as light as possible.

Of course there is also an argument that, due to the different shape of the contact patch, 29ers have more grip so you can run a narrower tyre (reducing the weight penalty). Then you have the fact that people often fit lighter rims to 29ers, but that’s often just giving up stiffness and longevity to save a bit on the weight. And of course you can always buy yourself out of the problem by fitting more expensive wheels so that you get the advantages of the extra radius with hardly any increase in weight.

world, the physics says bigger wheels slower / need more power

No it doesn’t. Physics says you can’t create or destroy energy so whatever power you put in you get back out.

No wheel size is ‘slower’ than an other.

but on virtually all courses, accelerating (to speed up, slow down or turn corners) is important. You need to think about what is the result of having heavier, larger diameter wheels in practical terms. Maybe if you want to achieve a speed record down a straight hill then OK, but back in the real world, the physics says bigger wheels slower / need more power

I have thought about that (and incidentally ride a 26″ MTB and 20″ BMX). When going downhill you have gravity as a power source and a bigger wheel can store more energy to pull you through the rough stuff, but requires more work from the rider to manoeuvre. I think the 29er’s contact patch is a better shape in the mud but the bigger wheel carries more mud weight and it’s harder to achieve good enough clearance around the BB. So for every pro there is a con. Choose what suits you and go and ride!

The 29’er was created to get rid of all the un sold short travel forks

I think that we should now discuss the merits of beards, pipes and slippers!